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Basic feed forward neural nets (MLPs) are essentially just computing sequences of matrix multiplications (with nonlinear activations in between), so this is in fact easy to code "directly" like you mentioned. The more difficult part is computing the gradients with respect to the parameter matrices (usually with backpropagation). However there ...


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This is precisely the optimal transportation problem. If both vectors are defined on the same space, you are trying to minimize the Wasserstein distance (which I think is equivalent to what N. Kiefer suggested). Associated to the Wasserstein distance / optimal transport cost is an optimal transport plan, which tells you how to transport the mass from vector ...


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There is not one answer to this question, but one could argue that transformers heavily rely on transforming each input into latent subspaces of queries, keys and values in order to generate attention score a pool of transformations of the attention vectors (multi-head) according to which models can capture richer interpretations as different sections of ...


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My sense is that everyone is pretending Intelligence doesn't have a grounded definition, from which all other definitions arise: Intelligence is a measure of utility in an action space μ(υ) It can be a relative measure, in relation to other rational agents, or absolute in relation to solved games (problems). An action space is any context, and formalized ...


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Just a few commonsensical remarks about why this kind of intelligence definition seems unable to capture the logic of life: Optimization only makes sense in a stationary environment. When many agents learn and interact, they are building a constantly changing environment. Survival and reproduction is the only thing that really matters, and it does not ...


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You are correct in the question that in RL terms chess a game of chess where the agent is one player, and the other player has an unknown state is a partially observable environment. Chess played like this is not a fully observable environment. I did not use the term "fully observable game" or "fully observable system" above , because ...


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A partially observable environment means it is from the agent's perspective that the agent observes the environment partially. At every time step, the agent takes action based on this partial observation. Based on the agent's action, the state of the environment changes, but the agent may not know all the changes.


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First, note that the current state does not determine the next state. What determines the next state are the dynamics of the environment, which, in the context of reinforcement learning and, in particular, MDPs, are encoded in the probability distribution $p(s', r \mid s, a)$. So, if the agent is in a certain state $s$, it could end up in another state $s'$, ...


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